To determine the cost of each jersey, [tex]\( x \)[/tex], and each pair of shorts, [tex]\( y \)[/tex], we start by examining the system of equations provided:
[tex]\[
\begin{cases}
12x + 12y = 156 \quad \text{(1)} \\
4x + 6y = 62 \quad \text{(2)}
\end{cases}
\][/tex]
We can simplify these equations step by step. First, divide equation (1) by 12:
[tex]\[
x + y = 13 \quad \text{(3)}
\][/tex]
Next, divide equation (2) by 2:
[tex]\[
2x + 3y = 31 \quad \text{(4)}
\][/tex]
Now, we have the simplified system of equations:
[tex]\[
\begin{cases}
x + y = 13 \quad \text{(3)} \\
2x + 3y = 31 \quad \text{(4)}
\end{cases}
\][/tex]
Let's use the substitution method to solve this system. Start by solving equation (3) for [tex]\( y \)[/tex]:
[tex]\[
y = 13 - x \quad \text{(5)}
\][/tex]
Substitute equation (5) into equation (4):
[tex]\[
2x + 3(13 - x) = 31
\][/tex]
Expand and simplify:
[tex]\[
2x + 39 - 3x = 31 \\
- x + 39 = 31 \\
- x = -8 \\
x = 8
\][/tex]
So, the cost of each jersey, [tex]\( x \)[/tex], is:
[tex]\[
x = 8
\][/tex]
Thus, the cost of each jersey is [tex]$\$[/tex]8[tex]$. From the provided options, the correct choice is:
\[
\$[/tex]8
\]
